A locker code is made of 4 letters taken from the six letters A, B, C, D, E and F, written in a fixed order. If no letter is repeated in a code, how many different codes can be made?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 360
In a code the order matters (ABCD and BACD are different codes), so this is an arrangement: \(^nP_r\).
First letter: 6 choices; second: 5; third: 4; fourth: 3 (no letter repeated)
Codes \(=\,^6P_4=6\times5\times4\times3=360\)
Why the other options are incorrect
Option (1) 15 — Incorrect. This is \(^6C_4\), which only chooses the 4 letters and ignores their order.
Option (2) 1296 — Incorrect. This is \(6^4\), the count when letters may be repeated.
Option (4) 720 — Incorrect. This is \(6!\), the count for codes using all 6 letters.